House training problem

About 4 months ago, we adopted 2 dogs from the SPCA. We love and enjoy both dogs (a Male Golden retriever and a female Jack Russel/Dachund mix).
But we have a problem. The Female Mix is not 100% house broken. And the problem is in communication.
She will bark incessantly when she wants IN from outside, but will not bark to go outside. When we are awake, we have learned her "signs" and have little trouble. But after we've gone to sleep, or if we are away, the dog will happily (it seems) use our carpets for any "business" she needs. We do not leave our dogs unattented for long periods and have had 0 problems w/the Golden in this regard.
It's a sweet dog, but it's come down to a showdown. Either the dog "gets w/the program" or she won't live here anymore. Looking for suggestions that we might try to help her.

Your little female may have been chastised for waking her former owners.

I've never used crate training, but from what you've said, your little one might benefit greatly from night time crating.

Brattina's got a lot of expertise in crate training; hopefully she'll check in on this thread.

First off I'd like to thank you for adopting a dog from the SPCA!

During the day time it seems like you're doing an okay job with the house training, and it sounds like crate training could work well for you. Even restricting the dog to one room (the kitchens a good one if it has tile floor that will be easy to clean just in case). Dogs are naturally clean animals and will avoid going in their den as long as they can. I'll write more later, sorry I got to go